THE Qn,k,m GRAPH: A COMMON GENERALIZATION OF VARIOUS POPULAR INTERCONNECTION NETWORKS

Abstract

The star graph and the alternating group graph were introduced as competitive alternatives to the hypercube, and they are indeed superior over the hypercube under many measures. However, they do suffer from scaling issues. To address this, different generalizations, namely, the (n,k)-star graph and the arrangement graph were introduced to address this shortcoming. From another direction, the star graph was recognized as a special case of Cayley graphs whose generators can be associated with a tree. Nevertheless, all these networks appear to be very different and yet share many properties. In this paper, we will solve this mystery by providing a common generalization of all these networks. Moreover, we will show that these networks have strong connectivity properties.